DO NOT BUY: Rylai's Crystal Scepter, Tear of the Goddess, Archangel's Staff, Abyssal Scepter, Deathfire Grasp, Haunting Guise, Liandry's Torment, Will of the Ancients, Rod of Ages. If you need to buy Lich Bane, it's OK but try avoiding it.
The reason you don't need those items is because some of them don't go according to how a Lux player should be. For Example:
-Abyssal Scepter is for melee or small ranged AP champions that need to stay close to the enemies in order to do damage. As Lux, you should always stay in the back and poke as much as you can, shielding as much of your team mates as you can also.
-Rod of Ages: As Lux, you'll try to stay in the back most of the time, there fore you don't need all the health that it proportions. If you usually buy this item because of the mana of AP it grants over time, as Lux that won't really make a difference. And the mana that it gives you will be replaced by Athene's Unholy Grail.